Equidistribution of saddle periodic points for H\'enon-like maps
Dynamical Systems
2025-02-28 v1 Complex Variables
Abstract
We prove that under the natural assumption over the dynamical degrees, the saddle periodic points of a H\'enon-like map in any dimension equidistribute with respect to the equilibrium measure. Our work is a generalization of results of Bedford-Lyubich-Smillie, Dujardin and Dinh-Sibony along with improvements of their techniques. We also investigate some fine properties of Green currents associated with the map. On the pluripotential-theory side, in our non-compact setting, the wedge product of two positive closed currents of complementary bi-degrees can be defined using super-potentials and the density theory. We prove that these two definitions are coherent.
Cite
@article{arxiv.2502.20103,
title = {Equidistribution of saddle periodic points for H\'enon-like maps},
author = {Muhan Luo and Qi Zhou},
journal= {arXiv preprint arXiv:2502.20103},
year = {2025}
}